Solve the System of Inequalities -2>=-x-7 and -x-7>-12

Add ${\displaystyle 7}$ to both sides of the inequality.

${\displaystyle -x\le -2+7}$ and ${\displaystyle -x-7>-12}$

Add ${\displaystyle -2}$ and ${\displaystyle 7}$.

${\displaystyle -x\le 5}$ and ${\displaystyle -x-7>-12}$

Divide each term in ${\displaystyle -x\le 5}$ by ${\displaystyle -1}$. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

${\displaystyle \frac{-x}{-1}\ge \frac{5}{-1}}$ and ${\displaystyle -x-7>-12}$

Simplify the left side.

${\displaystyle x\ge \frac{5}{-1}}$ and ${\displaystyle -x-7>-12}$

Simplify the right side.

${\displaystyle x\ge -5}$ and ${\displaystyle -x-7>-12}$

Add ${\displaystyle 7}$ to both sides of the inequality.

${\displaystyle x\ge -5}$ and ${\displaystyle -x>-12+7}$

Add ${\displaystyle -12}$ and ${\displaystyle 7}$.

${\displaystyle x\ge -5}$ and ${\displaystyle -x>-5}$

Divide each term in ${\displaystyle -x>-5}$ by ${\displaystyle -1}$. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

${\displaystyle x\ge -5}$ and ${\displaystyle \frac{-x}{-1}<\frac{-5}{-1}}$

Simplify the left side.

${\displaystyle x\ge -5}$ and ${\displaystyle x<\frac{-5}{-1}}$

Simplify the right side.

${\displaystyle x\ge -5}$ and ${\displaystyle x<5}$